There are two states of the world (S1, S2) on a future date. There are two secur

Question

There are two states of the world (S1, S2) on a future date. There are two securities available to investors. Investors in "Security A" receive $50 in S and $150 in S2. Investors in "Security B" receive $100 in Si and have to pay $50 in S, "Security A" and "Security B" are traded at $90 and $5 respectively Compute the state prices s1 and s2. What is the price of risk-tree security in this economy Construct a security that pays $80 in Sh and $60 in S2. Compute its price. You are presented with an investment opportunity in a residential building. The

Explanation / Answer

Let the state price at S1 be p1 and at S2 be p2

Hence 90 (current price)= 50p1+150p2....(i)

similarly 5=100p1-50p2...(ii)

Solving above two equations now-

from equation (i) 9=5p1+15p2

=> 9-15p2=5p1

=>p1= 9-15p2

   5

putting p1 value in equation (ii)

1=20p1-10p2

1=20*(9-15p2) - 10p2

   5

1=36-60p2-10p2

70p2= 35

p2 = 35/70= 0.50

Hence p1=6/20= 0.30

Hence answer is 0.50 and 0.30 for S1 and S2 respectively.

Price of risk free security-

Formula-

p1+p2=1/(1+r)

=>0.50+0.30= 1/(1+r)

0.80+r=1

r= 0.20 or 20%

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